Algebra Examples

$f (x) = 8 x + 1$ , $g (x) = \sqrt{x}$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(8 x + 1) \cdot (\sqrt{x})$

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

$8 x \sqrt{x} + 1 \sqrt{x}$

Step 1.2.2

Multiply $\sqrt{x}$ by $1$ .

$8 x \sqrt{x} + \sqrt{x}$

Step 2

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4